Dark Radiation after Planck Najla Said,1 Eleonora Di Valentino,1 and Martina Gerbino1

arXiv:1304.6217v1 [astro-ph.CO] 23 Apr 2013

1

Physics Department and INFN, Universit` a di Roma “La Sapienza”, Ple Aldo Moro 2, 00185, Rome, Italy We present new constraints on the relativistic neutrino effective number Neff and on the Cosmic Microwave Background power spectrum lensing amplitude AL from the recent Planck 2013 data release. Including observations of the CMB large angular scale polarization from the WMAP satellite, we obtain the bounds Neff = 3.71 ± 0.40 and AL = 1.25 ± 0.13 at 68% c.l.. The Planck dataset alone is therefore suggesting the presence of a dark radiation component at 91.1% c.l. and hinting for a higher power spectrum lensing amplitude at 94.3% c.l.. We discuss the agreement of these results with the previous constraints obtained from the Atacama Cosmology Telescope (ACT) and the South Pole Telescope (SPT). Considering the constraints on the cosmological parameters, we found a very good agreement with the previous WMAP+SPT analysis but a tension with the WMAP+ACT results, with the only exception of the lensing amplitude. PACS numbers: 98.80.Es, 98.80.Jk, 95.30.Sf

I.

INTRODUCTION

The recent precise measurements of the Cosmic Microwave Background (CMB hereafter) temperature anisotropies released by the Planck collaboration [1] are providing the tightest constraints on cosmological parameters to date [2]. In this paper, we use this new dataset to constrain two parameters that affect the CMB “damping tail” regime, at small angular scales, namely the neutrino effective number Neff and the lensing amplitude AL , that, from previous experiments, have been reported as not consistent with the standard expectations [3]. We remind here that Neff effectively measures the number of relativistic degrees of freedom at recombination and is related to the energy density in relativistic “dark” particles ρν by: "

7 ρν = 8

4 11

43

# Neff ργ ,

(1)

where ργ is the CMB photon energy density, with value today ργ,0 ≈ 4.8 × 10−34 g cm−3 . In the standard scenario, assuming three relativistic neutrino families, the expected value is Neff = 3.046. Observation of a different value could point to new physics, related to the neutrino sector, such as non standard neutrino decoupling, sterile neutrinos, etc., or to even more exotic physics, such as axions, extra dimensions, early dark energy (see e.g. [5], [4] and references therein). On the other hand, the AL parameter is a phenomenological parameter introduced in [6], that simply rescales the lensing potential: C`φφ → AL C`φφ

(2)

where C`φφ is the power spectrum of the lensing field. The expected value for this parameter in the standard framework is AL = 1. A value different from one could

indicate either the presence of a systematic, or the presence of new physics (see e.g. [3] and [7]). The previous CMB measurements obtained by the Atacama Cosmology Telescope (ACT, [8]) and the South Pole Telescope (SPT, [9]), when combined with the latest observations from the WMAP satellite (WMAP9, [10]), have indeed provided different values for these two parameters, that are in tension at the level of two standard deviations. As showed in [3], the ACT dataset gives Neff = 2.85 ± 0.56 and AL = 1.64 ± 0.36 at 68% c.l., while the SPT dataset gives Neff = 3.72 ± 0.46 and AL = 0.85 ± 0.13 at 68% c.l.. Given this tension, it is certainly timely to investigate the constraints that can be obtained for Neff and AL from the new data from the Planck satellite. The Planck collaboration has already presented results in [2] on Neff and AL separately. Here we extend this analysis by varying Neff and AL simultaneously, i.e. taking into account the possible correlations between these two parameters as in [3], and by properly comparing the results with the previous ACT and SPT measurements in the Neff -AL plane. Our paper is simply organized as follows: in the next section we describe the analysis method, in Section III we present our results also considering Baryon Acoustic Oscillation (BAO) surveys and H0 measurements, while in Section IV we derive our conclusions.

II.

DATA ANALYSIS METHOD

Our main CMB dataset consists in the Planck public data release of March 2013 [1]. We compare this dataset with the theoretical models using the CAMspec likelihood version 6.2 for high multipoles and the commander version 4.1 likelihood for low multipoles [11]. We also consider the WMAP low-` likelihood for polarization [10]. This dataset is identical to the “PLANCK+WP” case presented in the Planck papers [2, 11]. For BAO surveys we include the following datasets: SDSS-DR7 [12] at redshift z = 0.35, SDSS-DR9 [13] at

2 Parameter Planck+WP WMAP9+SPT WMAP9+ACT Ωb h2 0.02306 ± 0.00051 0.02264 ± 0.00051 0.02283 ± 0.00052 Ω c h2 0.1239 ± 0.0054 0.1232 ± 0.0080 0.110 ± 0.010 θ 1.04124 ± 0.00077 1.0415 ± 0.0012 1.0412 ± 0.0025 τ 0.095 ± 0.015 0.088 ± 0.014 0.090 ± 0.014 ns 0.996 ± 0.018 0.982 ± 0.018 0.969 ± 0.019 log[1010 As ] 3.111 ± 0.034 3.169 ± 0.048 3.174 ± 0.045 Neff 3.71 ± 0.40 3.72 ± 0.46 2.85 ± 0.56 AL 1.25 ± 0.13 0.85 ± 0.13 1.64 ± 0.36 ΩΛ 0.736 ± 0.022 0.736 ± 0.023 0.728 ± 0.025 t0 [Gyr] 13.08 ± 0.38 13.14 ± 0.43 13.90 ± 0.55 Ωm 0.264 ± 0.022 0.264 ± 0.023 0.272 ± 0.025 H0 [km/s/Mpc] 74.9 ± 3.7 74.6 ± 3.7 69.9 ± 3.7 TABLE I. Constraints at 68% confidence level on cosmological parameters from our analysis using Planck+WP, WMAP9+SPT and WMAP9+ACT.

Planck+WP WMAP9+SPT WMAP9+ACT

1.0

0.8 Probability

Probability

0.8 0.6 0.4 0.2 0.0

Planck+WP WMAP9+SPT WMAP9+ACT

1.0

0.6 0.4 0.2

2

3

N

4

5

eff

0.0

0.5

1.0

1.5

AL

2.0

2.5

3.0

FIG. 1. Comparison of the results for Planck+WP, WMAP9+SPT and WMAP9+ACT datasets in terms of the 1-D posterior distribution functions for the parameters Neff (left) and AL (right).

z = 0.57 and WiggleZ [14] at z = 0.44, 0.60, and 0.73. Finally, we include the recent measurements for the Hubble constant H0 from the analysis of [15] and we refer to this dataset as HST. For the analysis method we use the publicly available Monte Carlo Markov Chain package cosmomc [16] which relies on a convergence diagnostic based on the Gelman and Rubin statistic. We use the latest version (March 2013) which includes the support for the Planck Likelihood Code v1.0 (see http://cosmologist.info/ cosmomc/). The plots shown in this work are obtained via the python codes included in the cosmomc package. We run over the six-dimensional space of standard cosmological parameters: the baryon and cold dark matter densities Ωb and Ωc , the ratio of the sound horizon

to the angular diameter distance at decoupling θ, the reionization optical depth τ , the scalar spectral index nS , and the overall normalization of the spectrum AS at k = 0.05 Mpc−1 . We consider purely adiabatic initial conditions and we impose spatial flatness. In addiction to these parameters we let the number of neutrinos species (assumed massless) Neff and the lensing amplitude parameter AL to vary, assuming the following flat priors: 1.047 ≤ Neff ≤ 10 and 0.0 ≤ AL ≤ 4.0. In our runs, we also marginalise over the foreground parameters as in [2, 11]. Since the correlations between the cosmological and foreground parameters is minimal, we do not report their values in this paper. The posteriors on foregrounds are in excellent agreement with those reported in [2].

3 straints in the 2-D Neff − AL plane. As we can see, the Planck+WP constraint on Neff is in impressive agreement with the previous WMAP9+SPT constraint and in tension with the WMAP9+ACT value. On the other hand, the constraint on AL from Planck+WP is in better agreement with the WMAP9+ACT result but also consistent with the WMAP9+SPT constraint. It is also interesting to note that the Planck+WP dataset is in general in better agreement with the WMAP9+SPT dataset than the WMAP9+ACT on most of the parameters as the Hubble constant H0 , the matter density Ωm and the scalar spectral index nS . This could appear as in contradiction with the results presented in [2] where, on the contrary, a better agreement with the WMAP9+ACT dataset was reported. The reason of this different conclusion is due to the fact that while in [2] the comparison of Planck with ACT and SPT has been done by fixing AL = 1, here we let this parameter to vary freely. A similar conclusion has been reached by the SPT collaboration [17]. FIG. 2. Comparison of the 2-D posterior distribution function from the Planck+WP, WMAP9+ACT and WMAP9+SPT datasets in the Neff − AL plane.

III. A.

RESULTS

CMB data only

We first discuss our results obtained using the Planck+WP dataset. Posteriors on the cosmological parameters are shown in the first column of Table I. As we can see, the Planck+WP dataset provides an indication for a larger value of both Neff and AL , with Neff = 3.71 ± 0.40 and AL = 1.25 ± 0.13 at 68% c.l.. The constraints on Neff reported by the Planck collaboration for the same dataset is Neff = 3.51 ± 0.39 at 68% c.l.. However, this constraint is obtained with the condition AL = 1. The slightly larger value obtained in our analysis clearly shows that there is a small correlation between these two parameters and that fixing AL = 1 could slightly bias the constraints on Neff to smaller values. It is interesting to compare these results with the ones previously obtained in [3] for the ACT and SPT datasets, as shown in Table I. As we can see, the Planck+WP result on Neff is perfectly consistent with the WMAP9+SPT constraint of Neff = 3.72 ± 0.46, while there is a tension with the WMAP9+SPT result on AL = 0.85±0.13. Viceversa, the WMAP9+ACT constraint Neff = 2.85 ± 0.56 is clearly in tension with the Planck+WP result, while there is a better agreement with the bound on the lensing parameter AL = 1.64 ± 0.36. In order to better demonstrate the consistency between these datasets, we plot in Figure 1 the 1-D posterior distribution function for AL and Neff coming from these three analyses, while in Figure 2 we report the con-

B.

Adding BAO and HST

In this section we include the HST and BAO datasets. We report the results obtained from the Planck+WP+HST, Planck+WP+BAO and Planck+WP+HST+BAO analyses in the three columns of Table II, respectively. For the sake of brevity, we refer to the Planck+WP dataset as “CMB”. We show the 1-D posterior probability distributions for Neff and AL in Figure 3 and the 2-D confidence regions for Neff and AL in Figure 4 for all the dataset combinations discussed: CMB+HST, CMB+BAO and CMB+BAO+HST. Our results are in perfect agreement with those already presented in [2]. In fact, the introduction of the BAO dataset tends to drag down both the value of Neff and AL , i.e. to a better consistency with the standard expectation; on the other hand, the inclusion of the HST dataset preserves the Planck+WP mean values of parameters, reducing the error bars and therefore increasing the hints for new physics. In particular, for the CMB+HST case, both Neff and AL assume larger values at more than 95% confidence level. When both BAO and HST are combined, the final effect is to lower the value of AL = 1.17 ± 0.10, which however is still not in full agreement with the expected value of unity, and to lower the number of neutrinos species as well, giving Neff = 3.56 ± 0.27, which also remains at almost 2σ away from the standard value.

IV.

CONCLUSIONS

In this brief paper we have reported new joint constraints on the neutrino effective number Neff and the CMB lensing amplitude AL from the new Planck dataset.

4 Parameter CMB+HST CMB+BAO CMB+BAO+HST Ωb h2 0.022953 ± 0.00035 0.02246 ± 0.00031 0.02262 ± 0.00028 Ω c h2 0.1234 ± 0.0050 0.1232 ± 0.0053 0.1260 ± 0.0049 θ 1.04123 ± 0.00077 1.04112 ± 0.00078 1.04085 ± 0.00075 τ 0.094 ± 0.014 0.087 ± 0.013 0.089 ± 0.013 ns 0.992 ± 0.011 0.974 ± 0.011 0.9815 ± 0.0088 log[1010 As ] 3.108 ± 0.030 3.093 ± 0.030 3.103 ± 0.029 Neff 3.63 ± 0.27 3.35 ± 0.31 3.56 ± 0.27 AL 1.24 ± 0.12 1.16 ± 0.10 1.17 ± 0.10 ΩΛ 0.733 ± 0.014 0.706 ± 0.011 0.7119 ± 0.0094 t0 [Gyr] 13.15 ± 0.23 13.47 ± 0.28 13.27 ± 0.23 Ωm 0.267 ± 0.014 0.294 ± 0.011 0.2881 ± 0.0094 H0 [km/s/Mpc] 74.0 ± 2.0 70.4 ± 1.9 71.8 ± 1.6 TABLE II. Constraints at 68% confidence level on cosmological parameters from our analysis using CMB+HST, CMB+BAO and CMB+BAO+HST.

CMB CMB+HST CMB+BAO CMB+BAO+HST

1.0

0.8

Probability

Probability

0.8 0.6 0.4 0.2 0.0

CMB CMB+HST CMB+BAO CMB+BAO+HST

1.0

0.6 0.4 0.2

2.4

3.0

3.6

N

4.2

4.8

eff

0.0

0.8

1.0

1.2

AL

1.4

1.6

FIG. 3. Comparison of the 1-D posterior distribution functions from the CMB-only (Planck+WP), CMB+HST, CMB+BAO and CMB+BAO+HST datasets for Neff (left) and AL (right).

We have shown that the Planck+WP dataset is hinting for both a presence of dark radiation (at the level of 91.1%) and for an anomalous amplitude for the lensing parameter (at the level of 94.3%). The Planck+WP constraints on Neff and other parameters, such as the Hubble constant and the matter density, are in very good agreement with those obtained from the WMAP9+SPT dataset. It is clearly worth to note that two very different datasets provide an indication for a larger value of the effective neutrino number. In general, we found a tension on the derived parameters between the Planck+WP and the WMAP9+ACT datasets. This clearly indicates that the inclusion of the ACT dataset in a combined Planck+ACT has to be carefully considered.

is more consistent with the results obtained from the WMAP9+ACT dataset, which also provide a ∼ 2σ indication for a larger value. However, since the same signal is not found in the trispectrum analysis [18], the nature of this anomalous lensing amplitude needs further investigation. Moreover, our analysis clearly demonstrates a correlation between AL and the main cosmological parameters.

The anomalous lensing amplitude from Planck+WP

It will be probably duty of the next Planck data re-

The hints for new physics from the Planck+WP dataset are confirmed when the HST measurements are included and are weakened when the BAO dataset is considered. The CMB+HST+BAO analysis also suggests the presence of anomalous values but at smaller statistical significance.

5 lease, with the full mission and polarization data, to provide more precise, CMB only, constraints on the neutrino number and the lensing amplitude and to confirm or falsify these current hints for new physics from Planck.

Acknowledgements

FIG. 4. Comparison of the 2-D posterior distribution functions from the CMB-only, CMB+HST, CMB+BAO and CMB+BAO+HST datasets in the Neff −AL parameters plane.

[1] P. A. R. Ade et al. [Planck Collaboration], arXiv:1303.5062 [astro-ph.CO]. [2] P. A. R. Ade et al. [Planck Collaboration], arXiv:1303.5076 [astro-ph.CO]. [3] E. Di Valentino, S. Galli, M. Lattanzi, A. Melchiorri, P. Natoli, L. Pagano and N. Said, arXiv:1301.7343 [astroph.CO]. [4] E. Di Valentino, A. Melchiorri and O. Mena, arXiv:1304.5981 [astro-ph.CO]. [5] M. Archidiacono, E. Calabrese and A. Melchiorri, Phys. Rev. D 84 (2011) 123008 [arXiv:1109.2767 [astroph.CO]]. [6] E. Calabrese, A. Slosar, A. Melchiorri, G. F. Smoot and O. Zahn, Phys. Rev. D 77, 123531 (2008) [arXiv:0803.2309 [astro-ph]]. [7] A. Marchini, A. Melchiorri, V. Salvatelli and L. Pagano, arXiv:1302.2593 [astro-ph.CO]. [8] J. L. Sievers, R. A. Hlozek, M. R. Nolta, V. Acquaviva, G. E. Addison, P. A. R. Ade, P. Aguirre and M. Amiri et al., arXiv:1301.0824 [astro-ph.CO]. [9] Z. Hou, C. L. Reichardt, K. T. Story, B. Follin, R. Keisler, K. A. Aird, B. A. Benson and L. E. Bleem et al., arXiv:1212.6267 [astro-ph.CO]. [10] C. L. Bennett, D. Larson, J. L. Weiland, N. Jarosik, G. Hinshaw, N. Odegard, K. M. Smith and R. S. Hill

It is a pleasure to thank Andrea Marchini and Valentina Salvatelli for helpful discussions.

et al., arXiv:1212.5225 [astro-ph.CO]. [11] P. A. R. Ade et al. [Planck Collaboration], arXiv:1303.5075 [astro-ph.CO]. [12] N. Padmanabhan, X. Xu, D. J. Eisenstein, R. Scalzo, A. J. Cuesta, K. T. Mehta and E. Kazin, arXiv:1202.0090 [astro-ph.CO]. [13] L. Anderson, E. Aubourg, S. Bailey, D. Bizyaev, M. Blanton, A. S. Bolton, J. Brinkmann and J. R. Brownstein et al., Mon. Not. Roy. Astron. Soc. 428, 1036 (2013) [arXiv:1203.6594 [astro-ph.CO]]. [14] C. Blake, T. Davis, G. Poole, D. Parkinson, S. Brough, M. Colless, C. Contreras and W. Couch et al., Mon. Not. Roy. Astron. Soc. 415, 2892 (2011) [arXiv:1105.2862 [astro-ph.CO]]. [15] A. G. Riess, L. Macri, S. Casertano, H. Lampeitl, H. C. Ferguson, A. V. Filippenko, S. W. Jha and W. Li et al., Astrophys. J. 730, 119 (2011) [Erratum-ibid. 732, 129 (2011)] [arXiv:1103.2976 [astro-ph.CO]]. [16] A. Lewis and S. Bridle, Phys. Rev. D 66, 103511 (2002) [astro-ph/0205436]. [17] Talk given by John Carlstrom at the 47 ESLAB Planck conference. http://www.rssd.esa.int/SA/PLANCK/ docs/eslab47/Session13_Wrap-up_and_Conclusions/ 47ESLAB_April_05_2013_15_10_Carlstrom.pdf [18] P. A. R. Ade et al. [Planck Collaboration], arXiv:1303.5077 [astro-ph.CO].

arXiv:1304.6217v1 [astro-ph.CO] 23 Apr 2013

1

Physics Department and INFN, Universit` a di Roma “La Sapienza”, Ple Aldo Moro 2, 00185, Rome, Italy We present new constraints on the relativistic neutrino effective number Neff and on the Cosmic Microwave Background power spectrum lensing amplitude AL from the recent Planck 2013 data release. Including observations of the CMB large angular scale polarization from the WMAP satellite, we obtain the bounds Neff = 3.71 ± 0.40 and AL = 1.25 ± 0.13 at 68% c.l.. The Planck dataset alone is therefore suggesting the presence of a dark radiation component at 91.1% c.l. and hinting for a higher power spectrum lensing amplitude at 94.3% c.l.. We discuss the agreement of these results with the previous constraints obtained from the Atacama Cosmology Telescope (ACT) and the South Pole Telescope (SPT). Considering the constraints on the cosmological parameters, we found a very good agreement with the previous WMAP+SPT analysis but a tension with the WMAP+ACT results, with the only exception of the lensing amplitude. PACS numbers: 98.80.Es, 98.80.Jk, 95.30.Sf

I.

INTRODUCTION

The recent precise measurements of the Cosmic Microwave Background (CMB hereafter) temperature anisotropies released by the Planck collaboration [1] are providing the tightest constraints on cosmological parameters to date [2]. In this paper, we use this new dataset to constrain two parameters that affect the CMB “damping tail” regime, at small angular scales, namely the neutrino effective number Neff and the lensing amplitude AL , that, from previous experiments, have been reported as not consistent with the standard expectations [3]. We remind here that Neff effectively measures the number of relativistic degrees of freedom at recombination and is related to the energy density in relativistic “dark” particles ρν by: "

7 ρν = 8

4 11

43

# Neff ργ ,

(1)

where ργ is the CMB photon energy density, with value today ργ,0 ≈ 4.8 × 10−34 g cm−3 . In the standard scenario, assuming three relativistic neutrino families, the expected value is Neff = 3.046. Observation of a different value could point to new physics, related to the neutrino sector, such as non standard neutrino decoupling, sterile neutrinos, etc., or to even more exotic physics, such as axions, extra dimensions, early dark energy (see e.g. [5], [4] and references therein). On the other hand, the AL parameter is a phenomenological parameter introduced in [6], that simply rescales the lensing potential: C`φφ → AL C`φφ

(2)

where C`φφ is the power spectrum of the lensing field. The expected value for this parameter in the standard framework is AL = 1. A value different from one could

indicate either the presence of a systematic, or the presence of new physics (see e.g. [3] and [7]). The previous CMB measurements obtained by the Atacama Cosmology Telescope (ACT, [8]) and the South Pole Telescope (SPT, [9]), when combined with the latest observations from the WMAP satellite (WMAP9, [10]), have indeed provided different values for these two parameters, that are in tension at the level of two standard deviations. As showed in [3], the ACT dataset gives Neff = 2.85 ± 0.56 and AL = 1.64 ± 0.36 at 68% c.l., while the SPT dataset gives Neff = 3.72 ± 0.46 and AL = 0.85 ± 0.13 at 68% c.l.. Given this tension, it is certainly timely to investigate the constraints that can be obtained for Neff and AL from the new data from the Planck satellite. The Planck collaboration has already presented results in [2] on Neff and AL separately. Here we extend this analysis by varying Neff and AL simultaneously, i.e. taking into account the possible correlations between these two parameters as in [3], and by properly comparing the results with the previous ACT and SPT measurements in the Neff -AL plane. Our paper is simply organized as follows: in the next section we describe the analysis method, in Section III we present our results also considering Baryon Acoustic Oscillation (BAO) surveys and H0 measurements, while in Section IV we derive our conclusions.

II.

DATA ANALYSIS METHOD

Our main CMB dataset consists in the Planck public data release of March 2013 [1]. We compare this dataset with the theoretical models using the CAMspec likelihood version 6.2 for high multipoles and the commander version 4.1 likelihood for low multipoles [11]. We also consider the WMAP low-` likelihood for polarization [10]. This dataset is identical to the “PLANCK+WP” case presented in the Planck papers [2, 11]. For BAO surveys we include the following datasets: SDSS-DR7 [12] at redshift z = 0.35, SDSS-DR9 [13] at

2 Parameter Planck+WP WMAP9+SPT WMAP9+ACT Ωb h2 0.02306 ± 0.00051 0.02264 ± 0.00051 0.02283 ± 0.00052 Ω c h2 0.1239 ± 0.0054 0.1232 ± 0.0080 0.110 ± 0.010 θ 1.04124 ± 0.00077 1.0415 ± 0.0012 1.0412 ± 0.0025 τ 0.095 ± 0.015 0.088 ± 0.014 0.090 ± 0.014 ns 0.996 ± 0.018 0.982 ± 0.018 0.969 ± 0.019 log[1010 As ] 3.111 ± 0.034 3.169 ± 0.048 3.174 ± 0.045 Neff 3.71 ± 0.40 3.72 ± 0.46 2.85 ± 0.56 AL 1.25 ± 0.13 0.85 ± 0.13 1.64 ± 0.36 ΩΛ 0.736 ± 0.022 0.736 ± 0.023 0.728 ± 0.025 t0 [Gyr] 13.08 ± 0.38 13.14 ± 0.43 13.90 ± 0.55 Ωm 0.264 ± 0.022 0.264 ± 0.023 0.272 ± 0.025 H0 [km/s/Mpc] 74.9 ± 3.7 74.6 ± 3.7 69.9 ± 3.7 TABLE I. Constraints at 68% confidence level on cosmological parameters from our analysis using Planck+WP, WMAP9+SPT and WMAP9+ACT.

Planck+WP WMAP9+SPT WMAP9+ACT

1.0

0.8 Probability

Probability

0.8 0.6 0.4 0.2 0.0

Planck+WP WMAP9+SPT WMAP9+ACT

1.0

0.6 0.4 0.2

2

3

N

4

5

eff

0.0

0.5

1.0

1.5

AL

2.0

2.5

3.0

FIG. 1. Comparison of the results for Planck+WP, WMAP9+SPT and WMAP9+ACT datasets in terms of the 1-D posterior distribution functions for the parameters Neff (left) and AL (right).

z = 0.57 and WiggleZ [14] at z = 0.44, 0.60, and 0.73. Finally, we include the recent measurements for the Hubble constant H0 from the analysis of [15] and we refer to this dataset as HST. For the analysis method we use the publicly available Monte Carlo Markov Chain package cosmomc [16] which relies on a convergence diagnostic based on the Gelman and Rubin statistic. We use the latest version (March 2013) which includes the support for the Planck Likelihood Code v1.0 (see http://cosmologist.info/ cosmomc/). The plots shown in this work are obtained via the python codes included in the cosmomc package. We run over the six-dimensional space of standard cosmological parameters: the baryon and cold dark matter densities Ωb and Ωc , the ratio of the sound horizon

to the angular diameter distance at decoupling θ, the reionization optical depth τ , the scalar spectral index nS , and the overall normalization of the spectrum AS at k = 0.05 Mpc−1 . We consider purely adiabatic initial conditions and we impose spatial flatness. In addiction to these parameters we let the number of neutrinos species (assumed massless) Neff and the lensing amplitude parameter AL to vary, assuming the following flat priors: 1.047 ≤ Neff ≤ 10 and 0.0 ≤ AL ≤ 4.0. In our runs, we also marginalise over the foreground parameters as in [2, 11]. Since the correlations between the cosmological and foreground parameters is minimal, we do not report their values in this paper. The posteriors on foregrounds are in excellent agreement with those reported in [2].

3 straints in the 2-D Neff − AL plane. As we can see, the Planck+WP constraint on Neff is in impressive agreement with the previous WMAP9+SPT constraint and in tension with the WMAP9+ACT value. On the other hand, the constraint on AL from Planck+WP is in better agreement with the WMAP9+ACT result but also consistent with the WMAP9+SPT constraint. It is also interesting to note that the Planck+WP dataset is in general in better agreement with the WMAP9+SPT dataset than the WMAP9+ACT on most of the parameters as the Hubble constant H0 , the matter density Ωm and the scalar spectral index nS . This could appear as in contradiction with the results presented in [2] where, on the contrary, a better agreement with the WMAP9+ACT dataset was reported. The reason of this different conclusion is due to the fact that while in [2] the comparison of Planck with ACT and SPT has been done by fixing AL = 1, here we let this parameter to vary freely. A similar conclusion has been reached by the SPT collaboration [17]. FIG. 2. Comparison of the 2-D posterior distribution function from the Planck+WP, WMAP9+ACT and WMAP9+SPT datasets in the Neff − AL plane.

III. A.

RESULTS

CMB data only

We first discuss our results obtained using the Planck+WP dataset. Posteriors on the cosmological parameters are shown in the first column of Table I. As we can see, the Planck+WP dataset provides an indication for a larger value of both Neff and AL , with Neff = 3.71 ± 0.40 and AL = 1.25 ± 0.13 at 68% c.l.. The constraints on Neff reported by the Planck collaboration for the same dataset is Neff = 3.51 ± 0.39 at 68% c.l.. However, this constraint is obtained with the condition AL = 1. The slightly larger value obtained in our analysis clearly shows that there is a small correlation between these two parameters and that fixing AL = 1 could slightly bias the constraints on Neff to smaller values. It is interesting to compare these results with the ones previously obtained in [3] for the ACT and SPT datasets, as shown in Table I. As we can see, the Planck+WP result on Neff is perfectly consistent with the WMAP9+SPT constraint of Neff = 3.72 ± 0.46, while there is a tension with the WMAP9+SPT result on AL = 0.85±0.13. Viceversa, the WMAP9+ACT constraint Neff = 2.85 ± 0.56 is clearly in tension with the Planck+WP result, while there is a better agreement with the bound on the lensing parameter AL = 1.64 ± 0.36. In order to better demonstrate the consistency between these datasets, we plot in Figure 1 the 1-D posterior distribution function for AL and Neff coming from these three analyses, while in Figure 2 we report the con-

B.

Adding BAO and HST

In this section we include the HST and BAO datasets. We report the results obtained from the Planck+WP+HST, Planck+WP+BAO and Planck+WP+HST+BAO analyses in the three columns of Table II, respectively. For the sake of brevity, we refer to the Planck+WP dataset as “CMB”. We show the 1-D posterior probability distributions for Neff and AL in Figure 3 and the 2-D confidence regions for Neff and AL in Figure 4 for all the dataset combinations discussed: CMB+HST, CMB+BAO and CMB+BAO+HST. Our results are in perfect agreement with those already presented in [2]. In fact, the introduction of the BAO dataset tends to drag down both the value of Neff and AL , i.e. to a better consistency with the standard expectation; on the other hand, the inclusion of the HST dataset preserves the Planck+WP mean values of parameters, reducing the error bars and therefore increasing the hints for new physics. In particular, for the CMB+HST case, both Neff and AL assume larger values at more than 95% confidence level. When both BAO and HST are combined, the final effect is to lower the value of AL = 1.17 ± 0.10, which however is still not in full agreement with the expected value of unity, and to lower the number of neutrinos species as well, giving Neff = 3.56 ± 0.27, which also remains at almost 2σ away from the standard value.

IV.

CONCLUSIONS

In this brief paper we have reported new joint constraints on the neutrino effective number Neff and the CMB lensing amplitude AL from the new Planck dataset.

4 Parameter CMB+HST CMB+BAO CMB+BAO+HST Ωb h2 0.022953 ± 0.00035 0.02246 ± 0.00031 0.02262 ± 0.00028 Ω c h2 0.1234 ± 0.0050 0.1232 ± 0.0053 0.1260 ± 0.0049 θ 1.04123 ± 0.00077 1.04112 ± 0.00078 1.04085 ± 0.00075 τ 0.094 ± 0.014 0.087 ± 0.013 0.089 ± 0.013 ns 0.992 ± 0.011 0.974 ± 0.011 0.9815 ± 0.0088 log[1010 As ] 3.108 ± 0.030 3.093 ± 0.030 3.103 ± 0.029 Neff 3.63 ± 0.27 3.35 ± 0.31 3.56 ± 0.27 AL 1.24 ± 0.12 1.16 ± 0.10 1.17 ± 0.10 ΩΛ 0.733 ± 0.014 0.706 ± 0.011 0.7119 ± 0.0094 t0 [Gyr] 13.15 ± 0.23 13.47 ± 0.28 13.27 ± 0.23 Ωm 0.267 ± 0.014 0.294 ± 0.011 0.2881 ± 0.0094 H0 [km/s/Mpc] 74.0 ± 2.0 70.4 ± 1.9 71.8 ± 1.6 TABLE II. Constraints at 68% confidence level on cosmological parameters from our analysis using CMB+HST, CMB+BAO and CMB+BAO+HST.

CMB CMB+HST CMB+BAO CMB+BAO+HST

1.0

0.8

Probability

Probability

0.8 0.6 0.4 0.2 0.0

CMB CMB+HST CMB+BAO CMB+BAO+HST

1.0

0.6 0.4 0.2

2.4

3.0

3.6

N

4.2

4.8

eff

0.0

0.8

1.0

1.2

AL

1.4

1.6

FIG. 3. Comparison of the 1-D posterior distribution functions from the CMB-only (Planck+WP), CMB+HST, CMB+BAO and CMB+BAO+HST datasets for Neff (left) and AL (right).

We have shown that the Planck+WP dataset is hinting for both a presence of dark radiation (at the level of 91.1%) and for an anomalous amplitude for the lensing parameter (at the level of 94.3%). The Planck+WP constraints on Neff and other parameters, such as the Hubble constant and the matter density, are in very good agreement with those obtained from the WMAP9+SPT dataset. It is clearly worth to note that two very different datasets provide an indication for a larger value of the effective neutrino number. In general, we found a tension on the derived parameters between the Planck+WP and the WMAP9+ACT datasets. This clearly indicates that the inclusion of the ACT dataset in a combined Planck+ACT has to be carefully considered.

is more consistent with the results obtained from the WMAP9+ACT dataset, which also provide a ∼ 2σ indication for a larger value. However, since the same signal is not found in the trispectrum analysis [18], the nature of this anomalous lensing amplitude needs further investigation. Moreover, our analysis clearly demonstrates a correlation between AL and the main cosmological parameters.

The anomalous lensing amplitude from Planck+WP

It will be probably duty of the next Planck data re-

The hints for new physics from the Planck+WP dataset are confirmed when the HST measurements are included and are weakened when the BAO dataset is considered. The CMB+HST+BAO analysis also suggests the presence of anomalous values but at smaller statistical significance.

5 lease, with the full mission and polarization data, to provide more precise, CMB only, constraints on the neutrino number and the lensing amplitude and to confirm or falsify these current hints for new physics from Planck.

Acknowledgements

FIG. 4. Comparison of the 2-D posterior distribution functions from the CMB-only, CMB+HST, CMB+BAO and CMB+BAO+HST datasets in the Neff −AL parameters plane.

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It is a pleasure to thank Andrea Marchini and Valentina Salvatelli for helpful discussions.

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